Comparing the Population Pharmacokinetics of and Acute Kidney Injury Due to Polymyxin B in Chinese Patients with or without Renal Insufficiency

Despite excellent bactericidal effect, dosing adjustment of polymyxin B for patients with renal insufficiency and polymyxin B-related nephrotoxicity is still a major concern to clinicians. The aim of this study was to compare the population pharmacokinetics (PK) properties of polymyxin B in Chinese patients with different renal functions and to investigate the relationship between PK parameters and polymyxin B-related acute kidney injury (AKI). A total of 37 patients with normal renal function (creatinine clearance ≥ 80 ml/min) and 33 with renal insufficiency (creatinine clearance < 80 ml/min) were included.

ABSTRACT

Despite excellent bactericidal effect, dosing adjustment of polymyxin B for patients with renal insufficiency and polymyxin B-related nephrotoxicity is still a major concern to clinicians. The aim of this study was to compare the population pharmacokinetics (PK) properties of polymyxin B in Chinese patients with different renal functions and to investigate the relationship between PK parameters and polymyxin B-related acute kidney injury (AKI). A total of 37 patients with normal renal function (creatinine clearance ≥ 80 ml/min) and 33 with renal insufficiency (creatinine clearance < 80 ml/min) were included. In the two-compartment population PK models, the central compartment clearance (CL) (2.19 liters/h versus 1.58 liters/h; P < 0.001) and intercompartmental clearance (Q) (13.83 liters/h versus 10.28 liters/h; P < 0.001) values were significantly different between the two groups. The simulated values for AUC across 24 h at steady state (AUC_ss,24h) for patients with normal renal function were higher than those for patients with renal insufficiency. However, renal dosing adjustment of polymyxin B seemed not to be necessary. In addition, during the treatment, AKI occurred in 23 (32.86%) patients. The polymyxin B AUC_ss,24h in patients with AKI was significantly higher than that in patients without AKI (108.66 ± 70.10 mg · h/liter versus 66.18 ± 34.79 mg · h/liter; P = 0.001). Both the receiver operating characteristic (ROC) curve and logistic regression analysis showed that an AUC_ss,24h of >100 mg · h/liter was a good predictor for the probability of nephrotoxicity.

INTRODUCTION

The emergence of multidrug-resistant (MDR) Gram-negative bacteria has become an important clinical problem due to high morbidity and mortality worldwide (1). The lack of effective antibiotics and therapy against life-threatening MDR Gram-negative bacteria has prompted the reuse of the older antibiotic group the polymyxins, including colistin and polymyxin B (2, 3). Polymyxin B belongs to the polypeptide antibiotics, primarily acts on Gram-negative bacterial cell membrane phospholipids, and produces a disruptive physicochemical effect, leading to permeability changes in the bacterial cell outer membrane (2, 4). Despite the drug’s excellent bactericidal effect, polymyxin B-related nephrotoxicity is still a major concern to clinicians. It has been reported that the rate of acute kidney injury (AKI) in patients receiving polymyxin B goes up to 14 to 60% with regular dose (5, 6).

Contemporary studies have demonstrated that the ratio of the area under concentration-time curve to the MIC (fAUC/MIC) as the pharmacokinetic/pharmacodynamic (PK/PD) index is well correlated with polymyxin efficacy (7–9) and that the AUC is associated with polymyxin-related nephrotoxicity (10–12). Based on the above research, a target for AUC across 24 h at steady state (AUC_ss,24h) of 50 to 100 mg ⋅ h/liter, corresponding to an average steady-state plasma concentration (C_ss,avg) of 2 to 4 mg/liter, is recommended for polymyxin B therapeutic drug monitoring (TDM) (13, 14). However, it is worth noting that few PK/PD data are available for polymyxin B, especially for patients with renal insufficiency (15–21). According to FDA package inserts, polymyxin B doses should be reduced for patients with renal insufficiency, which is inconsistent with the recommendation provided by international consensus guidelines for the optimal use of polymyxins (14, 22). With a wide range of creatinine clearances (CL_CR), our previous study found that renal function could slightly influence polymyxin B clearance (18). However, observations regarding the influence of CL_CR on population PK parameters of polymyxin B are inconsistent across the literature (15, 19, 20). Therefore, it is necessary to investigate potential PK variability of polymyxin B in patients with different kidney function.

Additionally, clinical pharmacokinetic/toxicodynamic (PK/TD) data for polymyxin B were also scarce. For the absence of exposure-toxicity data, the target polymyxin B exposure was simulated based on data derived from a pharmacometrics nephrotoxicity meta-analysis and colistin (13, 14). No direct clinical data about the exposure-AKI of polymyxin B are available at present.

In this study, we retrospectively analyzed 70 polymyxin B-treated patients with MDR Gram-negative bacterial infections. The objectives were to assess the PK variability of polymyxin B in patients with and without renal insufficiency and to evaluate the exposure in predicting polymyxin B-related nephrotoxicity.

RESULTS

Patients.

Overall, a total of 70 patients contributing 462 plasma samples, including 46 reported in our previous report (18), were enrolled in the analysis. Table 1 summarizes the demographic and clinical information of the patients. Among them, 37 patients had normal renal function (CL_CR ≥ 80 ml/min) and 33 patients had renal insufficiency (CL_CR < 80 ml/min). There was no significant difference in baseline characteristics between two groups except serum creatinine (SCr), CL_CR, and glomerular filtration rate (GFR).

TABLE 1.

Demographic characteristics of patients

Characteristic	Value for patients with CLCR of:		P
	≥80 ml/min (n = 37)	<80 ml/min (n = 33)
Sex, no. (%)
Male	31 (83.8)	27 (81.8)	0.828
Female	6 (26.2)	6 (28.2)
Age (yrs), mean ± SD	47.3 ± 17.7	54.2 ± 17.5	0.107
Wt (kg), mean ± SD	68.6 ± 11.6	66.9 ± 11.1	0.528
Creatinine clearance (ml/min), median (range)	123.3 (81.6–315.2)	42.0 (15.6–77.6)	<0.001
Serum creatinine (μmol/liter), median (range)	50.0 (21.0–116.0)	163.0 (77.0–387.0)	<0.001
GFRa (ml/min ⋅ 1.73m2), median (range)	113.4 (70.2–165.02)	36.7 (15.2–89.9)	<0.001
Daily dose/body wt (mg/kg), mean ± SD	2.0 ± 0.5	2.0 ± 0.5	0.940
Duration of therapy (days), median (range)	14 (4–54)	12 (4–44)	0.617
Sepsis/septic shock	17	16	0.832
Other nephrotoxic drugs	14	18	0.161
Vancomycin	4	4
Amphotericin B	1	4
Aminoglycoside	1	1
Immunosuppressant	2	6
Furosemide	9	7
Infection sites
Lung	20	18
Bloodstream	10	9
Abdomen	6	2
Intracranial	6	1
Others	6	4
Pathogenic bacterial cultures
Acinetobacter baumannii	16	11
Klebsiella pneumoniae	19	11
Pseudomonas aeruginosa	6	6
Escherichia coli	2	5
Others	2	2

^aGFR, glomerular filtration rate.

Population PK model.

Based on our previous work (18), a two-compartmental model with a proportional option was chosen as the base model. For both groups, no covariate effect was identified during the modeling. However, for the normal renal function group model, correlations between central compartment clearance (CL), volume of distribution (V), and volume of peripheral compartment distribution (V₂) were observed and therefore incorporated into off-diagonal elements of variance-covariance matrix (change in objective function value [ΔOFV] = 27.21; P < 0.01). As to the renal insufficiency group model, there was too little individual variation of intercompartmental clearance (Q) (shrinkage factor > 0.5), so it was not taken into the model. Additionally, correlations between CL, V, and V₂ were observed, and these were incorporated into off-diagonal elements of variance-covariance matrix (ΔOFV = 17.91; P < 0.01). Finally, the goodness-of-fit plots, prediction-corrected visual predictive check (VPC), and bootstrap analysis were used to assess the adequacy and precision of the two final models.

In prediction-corrected VPC diagrams (Fig. 1), most of the observed data were within 95% prediction percentiles. In goodness-of-fit plots of two final models (see Fig. S1 in the supplemental material), no apparent systematic bias was observed, and the plots were normally distributed. Bootstrap results (Table S1) indicated qualified precision for the final population PK models. Accordingly, the final population PK model parameters are shown in Table 2. For patients with normal renal function, the CL (2.19 liters/h versus 1.58 liters/h; P < 0.001) and Q (13.83 liters/h versus 10.28 liters/h; P < 0.001) were significantly different from the values for patients with renal insufficiency.

FIG 1.

Prediction-corrected visual predictive check of the final model. (A) Patients with normal renal function; (B) patients with renal insufficiency. Red lines represent the 5th, 50th, and 95th percentiles of the observed concentrations, the shaded areas represent the 90% confidence intervals of the 5th, 50th, and 95th percentiles of the simulated concentrations, and the dots represent the prediction-corrected observation concentration. DV, observed dependent variable; IVAR, independent variable.

TABLE 2.

Parameter estimates of the final population pharmacokinetic models^a

Parameter	Normal renal function group					Renal insufficiency group
	Estimate	SE	CV (%)	95% CI	Shrinkage (%)	Estimate	SE	CV (%)	95% CI	Shrinkage (%)
tvV	6.87	1.65	24.06	3.62–10.13	9.02	6.98	1.12	15.99	4.78–9.18	10.18
tvV2	11.97	1.73	14.47	8.56–15.38	1.33	10.57	1.80	17.0	7.03–14.12	13.28
tvCL	2.19	0.17	7.75	1.85–2.52	7.32	1.58	0.14	8.99	1.30–1.87	8.86
tvQ	13.83	4.33	31.29	5.30–22.35	26.77	10.28	1.42	13.83	7.47–13.08	NA
Interindividual variability
ω2V	0.78	0.31	39.74	NA	NA	0.38	0.16	42.11	NA	NA
ω2CL	0.22	0.05	22.73	NA	NA	0.26	0.07	26.92	NA	NA
ω2V2	0.32	0.14	52.94	NA	NA	0.74	0.27	36.49	NA	NA
ω2Q	0.68	0.28	41.18	NA	NA	NA	NA	NA	NA	NA
CorrV-CL	0.57	0.09	15.79	NA	NA	0.75	0.09	12.0	NA	NA
CorrCL-V2	0.76	0.06	7.89	NA	NA	NA	NA	NA	NA	NA
CorrV-V2	0.83	0.13	15.66	NA	NA	0.46	0.13	28.26	NA	NA
Residual variability (σ)
SD	0.13	0.01	6.22	0.11–0.14	NA	0.10	0.01	6.44	0.09–0.12	NA

^aCV, confidence of variation; CI, confidence interval; tvV, typical value of central compartment distribution volume (V); V₂, peripheral compartment distribution volume; CL, central compartment clearance; Q, intercompartmental clearance (CL₂); ω²V, variance of the interindividual variability of V; CorrV-CL, correlation between random effects for V and CL; NA, not applicable.

Monte Carlo simulations.

Based on the above two final population PK models, the simulated 5th, 50th, and 95th quantiles of AUC_ss,24h on day 4 are shown in Table 3.

TABLE 3.

The simulated AUC_ss,24h of polymyxin B on day 4 for each simulated regimen at the 10th, 50th, and 90th percentiles of body weight^a

Maintenance dose	Wt (kg)	Simulated AUCss,24h
		Normal renal function group			Renal insufficiency group
		P5	P50	P95	P5	P50	P95
1.25 mg/kg, q12h	55	25.37	60.21	138.37	32.45	82.45	201.54
	65	30.86	71.37	162.44	39.87	97.46	230.17
	80	39.25	90.54	203.23	48.92	125.79	277.18
1.5 mg/kg, q12h	55	29.48	73.77	173.23	43.42	102.67	249.01
	65	36.30	86.70	198.44	45.74	120.17	299.14
	80	44.81	106.49	230.36	60.06	147.72	347.16

^aAUC_ss,24h, area under the plasma concentration-time curve across 24 h at steady state; P5, 5th percentile; P50, 50th percentile; P95, 95th percentile; q12h, every 12 h.

Drug exposure and AKI.

Polymyxin B trough concentrations at steady state (C_ss,min) varied, with a wide range, from 0.27 to 8.42 μg/ml. The mean AUC_ss,24h was 80.14 ± 52.70 mg · h/liter, with a range of 20.50 to 253.30 mg · h/liter, corresponding to the mean C_ss,avg of 3.33 ± 2.20 μg/ml, with a range of 0.85 to 10.55 μg/ml. The mean AUC_ss,24h of polymyxin B (68.63 ± 43.43 mg · h/liter) in the normal renal function group was lower than that (93.04 ± 59.52 mg · h/liter) in the renal insufficiency group (Fig. 2A). However, there was no difference between the two groups (P = 0.057). After the AUC was normalized to a daily dose of 1 mg/kg of body weight [AUC/(daily dose/body weight)], there was still no difference between the two groups (34.52 ± 18.88 mg · h/liter versus 45.86 ± 23.60 mg · h/liter; P = 0.094).

FIG 2.

Comparison of polymyxin B exposures (AUC_ss,24h) stratified by renal function (A) and by the incidence of acute kidney injury (AKI) (B). Data are means ± standard deviations; normalized AUC_ss,24h was adjusted to the dose/body weight. *, P < 0.05.

During the treatment, AKI occurred in 23 (32.86%) patients. Specifically, 11 (15.71%) were classified as at risk of renal dysfunction, 7 (10.0%) as having injury to the kidney, and 5 (7.14%) as having failure of kidney function. The median time to develop AKI was 5 days, with a range of 3 to 18 days. In the normal renal function group, 15 out of 37 (40.54%) patients developed AKI, which was not significantly different from the value of 8 out of 33 (24.24%; P = 0.147) in the renal insufficiency group. The average AUC_ss,24h of polymyxin B for development of AKI was 108.66 ± 70.10 mg · h/liter, which was significantly higher than that of 66.18 ± 34.79 mg · h/liter in patients without AKI (P = 0.001 [Fig. 2B]). After adjustment with the average daily dose/weight, the average normalized AUC_ss,24h of patients with AKI did not significantly differ from the values of patients without AKI (49.21 ± 29.50 mg · h/liter versus 35.80 ± 19.45 mg · h/liter; P = 0.057).

As shown in Fig. 3, the area under the ROC curve of AUC_ss,24h was the largest, indicating that AUC_ss,24h had the strongest correlation with AKI (area under the diagnostic curve [AUC_ROC] = 0.778; P = 0.001). In addition, C_ss,min also showed correlation with AKI (AUC_ROC = 0.704; P = 0.012). When the Youden indices were the largest (0.488 and 0.419), the corresponding optimal cutoff values of AUC_ss,24h and C_ss,min were 106.96 mg · h/liter and 2.25 μg/ml, respectively. The predictive sensitivities of the optimal cutoff values were 65.0% and 50.0% and the specificities were 83.8% and 91.9%, respectively. Logistic regression analysis (Fig. 4) showed that the regression equation of AUC_ss,24h was λ = −0.92 + 0.30 × log (x) and that of C_ss,min was λ = 0.25 + 0.23 × log (x). The AUC_ss,24h value of 100 mg · h/liter and C_ss,min of 2.23 mg/liter were associated with a 44.29% probability of AKI.

FIG 3.

The area under the ROC curve of polymyxin B exposure parameters in prediction of acute kidney injury.

FIG 4.

The probability of incidence of polymyxin B-related acute kidney injury under different values for AUC_ss,24h (A) and C_ss,min (B).

DISCUSSION

Due to limited clinical data, renal dose adjustments of polymyxin B remain controversial in the clinic (17, 22). In the present study, the population PK properties of polymyxin B in patients with different renal function were analyzed and compared. For PK parameter estimate (Table 2), the CL and Q values were significantly different between two groups (P < 0.001); however, the variance was still within a 2-fold range. Based on the Monte Carlo simulations (Table 3), the median AUC_ss,24h for patients with normal renal function was lower than that derived from patients with renal insufficiency. A 2-fold change in AUC is commonly accepted as the threshold justification for dosing adjustment (19), which suggests that the differences of population PK parameters between two groups are clinically insignificant and dosing adjustment in renal insufficiency seem not to be necessary. However, if administered according to the therapeutic window (14), for patients with normal renal function, the maintenance dose of 1.25 to 1.5 mg/kg twice daily would be sufficient; the maintenance dose for patients with renal dysfunction is 1.25 mg/kg twice daily.

In this study, both the AUC_ss,24h and normalized AUC_ss,24h of polymyxin B in the renal insufficiency group were higher than those in the normal renal function group (Fig. 2A); nevertheless, there was no difference between the two groups (P = 0.057 and 0.094). In another clinical study, Thamlikitkul et al. (16) reported that the AUC_ss,24h of polymyxin B in 14 insufficient renal patients (CL_CR < 80 ml/min) was slightly lower than that in 5 normal renal function patients (56.0 ± 17.5 mg · h/liter versus 63.5 ± 16.6 mg · h/liter; P = 0.42), which was inconsistent with our results. However, after adjusting the AUC_ss,24h for daily dose/weight, the result was in agreement with our study (16). Our results were also consistent with those reported for experimental animals, in which it was found that the drug exposure was elevated by approximately 30% in postrenal insufficiency rats compared to that in prerenal insufficiency rats (23).

It was reported that polymyxin B-induced nephrotoxicity was correlated with high dose, dosing interval, etc. (5, 24–28). Among these risk factors, the dosage was always considered to be the key factor (28). A multicenter prospective cohort study of 406 patients found that a daily dose of ≥150 mg was a risk factor for AKI (29). However, in this study, 69.57% (16 out of 23) patients with AKI had daily doses of ≥150 mg, which was comparable to 48.94% (23 out of 47) derived from patients without AKI (P = 0.103). Of note, the mean AUC_ss,24h of polymyxin B in patients with AKI was significantly higher than that in patients without AKI (P = 0.001 [Fig. 2B]). Furthermore, both the optimal cutoff of the ROC curve and logistic regression analysis showed that an AUC_ss,24h of >100 mg · h/liter was a good predictor for the probability of AKI (Fig. 3 and 4). Therefore, drug exposure could be more informative than drug dosage in predicting the likelihood/onset of AKI. On the basis of a pharmacometric meta-analysis of polymyxin B nephrotoxicity data, Lakota et al. also proposed an AUC_ss,24h of 100 mg · h/liter as a predictor for nephrotoxicity (13). This boundary was based on a target of a less than 40% nephrotoxicity incidence, which was consistent with the nephrotoxicity prevalence of 32.86% in this study.

In addition, among 23 patients with AKI, the AUC_ss,24h of 12 patients was lower than 100 mg · h/liter. This result indicated that other factors might contribute to AKI, such as serious underlying medical conditions and coadministration of nephrotoxic drugs (26). However, in this study, 11 patients with AKI had sepsis/septic shock and 10 were coadministered other nephrotoxic drugs, which was comparable to that in the patients without AKI (P = 0.938 and 0.793).

In the clinical setting, since obtaining multiple samples throughout a dosing interval to estimate AUC is not always feasible, C_ss,min was usually used instead of AUC to predict drug efficacy and toxicity (30, 31). In this study, there was a good correlation between AUC_ss,24h and C_ss,min (r² = 0.817). Consistent with the above AUC_ss,24h results, the mean C_ss,min in patients with AKI was much higher than that in patients without AKI (2.82 ± 2.07 mg/liter versus 1.41 ± 0.99 mg/liter; P = 0.004), and a C_ss,min of >2.23 mg/liter was strongly associated with the risk of AKI (Fig. 4). This suggested that C_ss,min also was a good indicator to predict polymyxin B-induced AKI.

There are several limitations to this study. First, due to the lack of sufficient sample size, a simple cutoff was used to separate the two groups, which could not reflect the actual clinical situation. Therefore, future studies should investigate the PK characteristics of polymyxin B using different thresholds of CL_CR. Second, the external validation of population PK models lacked a limited sample size. Third, besides AKI, other typical adverse effects of polymyxin B, such as neurotoxicity and skin pigmentation, did not evaluate due to the retrospective nature of this study. Finally, although we noted there was a good correlation between C_ss,min and polymyxin B-induced AKI, the therapeutic threshold based on C_ss,min was not investigated due to the lack of efficacy evaluation.

In conclusion, by comparing the population PK models for patients with and without renal insufficiency, it was found that the CL and Q values were significantly different. Nevertheless, based on the simulated AUC_ss,24h, the renal dosing adjustment of polymyxin B seemed not to be necessary. Besides, the mean AUC_ss,24h of polymyxin B in patients with AKI was significantly higher than that in patients without AKI, and an AUC_ss,24h of >100 mg · h/liter was a good predictor for the probability of AKI, which suggested that drug exposure could be informative in predicting the likelihood/onset of AKI.

MATERIALS AND METHODS

Study design.

Patients (age ≥ 18 years) who had received intravenous polymyxin B for ≥72 h (sulfate; polymyxin B for injection; Shanghai First Biochemical Pharmaceutical Co., Ltd.) for the treatment of MDR Gram-negative bacterial infection at the First Affiliated Hospital of Zhengzhou University between April 2018 and March 2020 were included. Patients on any form of renal replacement therapy and/or with fluctuant renal function (increase or decrease in serum creatinine of more than 50% 3 days before polymyxin B therapy) were excluded. The study protocol was approved by the hospital ethics committee review board (Zhengzhou University Medical Research and Ethics Committee, no. L2018K129). Written informed consent was obtained from all patients. For data analytics, normal renal function was defined as an estimated CL_CR of ≥80 ml/min before polymyxin B treatment, and renal insufficiency was defined as an estimated CL_CR of <80 ml/min. CL_CR was calculated according to the Cockcroft-Gault equation (32). Clinical data, including age, sex, weight, infected sites, pathogens, polymyxin B therapy, and laboratory data, were collected from electronic medical records.

Polymyxin B administration and assay.

In clinic practice, the loading dose of polymyxin B was 1.0 to 1.5 million IU (10,000 IU = 1 mg), and the maintenance dose was 50 to 100 mg twice daily according to the package inserts. The recommended infusion time was more than or equal to 1 h. Polymyxin B treatment at different clinical departments was at the discretion of their medical teams. Blood samples for polymyxin B TDM were obtained after at least 3 days of therapy. For each patient, during a dosing interval, 4 to 7 blood samples (2 ml into EDTA tubes) were collected immediately before starting the infusion and 0 to 1, 2 to 4, and 6 to 10 h after the infusion. All samples were centrifuged at 3,500 × g for 10 min. The supernatant was collected and stored at −80°C until analysis.

Polymyxin B plasma concentration was determined using validated liquid chromatography-tandem mass spectrometry (LC-MS/MS) as described previously (33). In brief, the calibration curves showed acceptable linearity over 0.2 to 10.0 μg/ml for polymyxin B1 and 0.05 to 2.5 μg/ml for polymyxin B2. The upper limit of quantification was extended to 20.0 μg/ml for polymyxin B1 and 5.0 μg/ml for polymyxin B2 after 4-fold dilution. The intra- and interbatch assay imprecision ranged from 0 to 13.93% for quality control samples, and their corresponding inaccuracy ranged from −10.87 to 11.13%. Since polymyxin B1 and B2 had similar structures, molecular weights, pharmacological activities, and pharmacokinetic characteristics, the plasma concentration of polymyxin B was summed from polymyxin B1 and B2 concentrations (34, 35).

Population PK modeling.

The population PK parameters were determined by one- or two-compartmental models performed using Phoenix NLME software (v7.0; Pharsight, Mountain View, CA). PK models were estimated by the first-order conditional estimation method (FOCE ELS). Model assessment criteria included the precision of parameter estimates (standard error), goodness-of-fit plots, and likelihood ratio test (-2 log likelihood [-2LL]). Basic parameters included the volume of central compartment distribution (V) and central compartment clearance (CL) for the one-compartment model and the volume of peripheral compartment distribution (V₂) and intercompartmental clearance (Q; CL₂) for the two-compartment model.

The modeling steps were consistent with our previous report (18). In brief, for the initial model, interindividual variability was described using an exponential-error model. Intraindividual variability (residual error) was described using an additive, proportional, or mixed (additive plus proportional) model. Then, the covariate (age, sex, body weight, and CL_CR) selection was evaluated using a stepwise process. By comparing with initial model, a drop of >3.84 (P = 0.05) of objective function value (OFV; -2LL) during forward selection and an increase of OFV of >6.63 (P = 0.01) during backward selection were the inclusion criteria for covariates. Subsequently, based on the scatterplot and ΔOFV (a drop of OFV of >6.63), the relevant population PK parameters were introduced into off-diagonal elements of the variance-covariance matrix to obtain the final model.

At last, the adequacy of the final model was assessed using goodness-of-fit plots. The model performance was evaluated by a prediction-corrected visual predictive check (VPC) with 1,000 replicates. Additionally, the precision of the parameter estimates was assessed using bootstrap analysis with 1,000 samples.

Monte Carlo simulations.

Based on the final population PK models, the plasma concentration-time profile of 1,000 individuals was simulated. The dose regimens were set at a 1.25- or 1.5-mg/kg maintenance dose twice daily, and body weight was selected as the 10th, 50th, and 90th percentiles of patients. The infusion rate was set as 50 mg/h, and the loading dose was 2.5 mg/kg.

Polymyxin B exposure and AKI.

The raw data were first estimated by Bayesian approach with the final population PK models and then calculated using noncompartmental analysis to obtain the area under the curve at steady state from 0 to 12h (AUC_ss,12h). To calculate AUC_ss,12h, the blood sample collected before infusion was regarded as the sample collected at 12 h. The AUC_ss,12h multiplied by 2 to obtain AUC_ss,24h, and C_ss,avg was obtained by dividing AUC by the interval time. The AKI was defined as an increase of >50% of serum creatinine (SCr) or a decrease of >25% of glomerular filtration rate (GFR) from baseline at any time between treatment initiation and 48 h after the end of polymyxin therapy. The increased SCr or decreased GFR was also confirmed by the next repeat determination. Further classified was according to the RIFLE criteria (32).

To develop ROC curves, the drug exposure parameters AUC_ss,24h, the trough and peak concentrations at steady state (C_ss,min and C_ss,max) were used as predictors of AKI. The area under the diagnostic curve (AUC_ROC) was calculated to evaluate the correlation between the above parameters and AKI. Furthermore, the AUC_ss,24h and C_ss,min were incorporated into the logistic regression model, and the exponential conversion was used to calculate the probability of polymyxin B-related AKI (36). The calculation formulas are shown in equations 1 and 2.

$${\lambda }_i={\theta }_1+{\theta }_2\times \text{log}\left(x\right)$$ (1)

$$P_i=\text{exp}\left({\lambda }_i\right)/\left[\text{1}+\text{exp}\left({\lambda }_i\right)\right]$$ (2)

where λ_i is the linear function of log-transformed x (AUC_ss,24h or C_ss,min), with θ₁ and θ₂ as intercept and slope, respectively. P_i was the logistic function representing the probability of AKI.

Statistical analysis.

Statistical analysis was performed with SPSS 26.0 (SPSS, IBM Company, Chicago, IL) software. Continuous variables are presented as means ± standard deviations if normally distributed and as medians (ranges) if abnormally distributed. Continuous variables were compared using the Student t test for normally distributed data and the Mann-Whitney U test for abnormally distributed data. Categorical variables were analyzed using the chi-square test (χ²) test. A P value of <0.05 was considered statistically significant.